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Trail_Builder
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this question is contained on a gcse past paper i am doing and i think I am approaching it from the wrong angle but have tried a few times and don't know where i am going wrong :( hope you can help
A bag contains (n+7) tennis balls.
n of the balls are yellow.
The other 7 balls are white.
John will take at random a ball from the bag.
He will look at its colour and then put it back in the bag.
part a) Bill states that the probability that John will take a white ball is 2/5
Prove that Bill's statement cannot be correct.
part b) After John has put the ball back into the bag, Mary will then take at random a ball from the bag.
She will note its colour.
Given the probability that John and Mary will take balls with different colours is 4/9, prove that 2n^2 - 35n + 98 = 0
a) (I think I got this bit right)
2/5 = 7/(n+7)
n+7 = 7/(2/5)
n+7 = 7/0.4
n+7 = 17.5
n = 10.5
Bill's statement cannot be write because there cannot be a non-interger number of balls.
b)
I did a probability tree thing and worked out there are 2 ways that they will have different colours, each with a 7n/(n+7) probability.
therefore, there is a 14n/(n+7) chance of them selecting different colours.
(this is where i might be going wrong)
so, 14n/(n+7) = 4/9
126n/(n+7) = 4
n+7 = 126n / 4
n+7 = 31.5n
7 = 30.5n
??
this is where i get stuck cause i realize i shouldn't being working out n should I?
is it i have to factorise it out somewhere? get it in quadradic form or whatever?
hope you can help
thnx
Homework Statement
A bag contains (n+7) tennis balls.
n of the balls are yellow.
The other 7 balls are white.
John will take at random a ball from the bag.
He will look at its colour and then put it back in the bag.
part a) Bill states that the probability that John will take a white ball is 2/5
Prove that Bill's statement cannot be correct.
part b) After John has put the ball back into the bag, Mary will then take at random a ball from the bag.
She will note its colour.
Given the probability that John and Mary will take balls with different colours is 4/9, prove that 2n^2 - 35n + 98 = 0
Homework Equations
The Attempt at a Solution
a) (I think I got this bit right)
2/5 = 7/(n+7)
n+7 = 7/(2/5)
n+7 = 7/0.4
n+7 = 17.5
n = 10.5
Bill's statement cannot be write because there cannot be a non-interger number of balls.
b)
I did a probability tree thing and worked out there are 2 ways that they will have different colours, each with a 7n/(n+7) probability.
therefore, there is a 14n/(n+7) chance of them selecting different colours.
(this is where i might be going wrong)
so, 14n/(n+7) = 4/9
126n/(n+7) = 4
n+7 = 126n / 4
n+7 = 31.5n
7 = 30.5n
??
this is where i get stuck cause i realize i shouldn't being working out n should I?
is it i have to factorise it out somewhere? get it in quadradic form or whatever?
hope you can help
thnx